DNS records get cached, as we have seen above. So if your DNS record is cached for IP address 1.2.3.4 and the service provider changes the record to 5.6.7.8, you will send traffic for your mapped apex domain to the wrong address until the record expires in all caching resolvers.
This is true for any cached request, not just an ALIAS. As a matter of fact, the way we implement the ALIAS record is to always attempt the lookup through an upstream caching resolver, so we are effectively behaving the same way a client sending the request directly to the caching resolver would.
You also potentially break geoIP optimisations because suddenly you request the IP address from the nameserver of your DNS provider, not from your actual location. This may even get you in trouble with location restricted services (think Unblock-Us, just not in an intended way).
With Anycast the results of geocaching can potentially be mitigated because the request will be resolved at an Anycast server near the client. As you add more